Measuring surface curvature

Abstract

A method of measuring surface curvature comprises forming an intensity distribution defined by Fresnel diffraction, wherein said intensity distribution is formed by electromagnetic radiation reflected from a surface, obtaining data for the intensity distribution and determining information relating to the curvature of the surface using the obtained data.

Many further modifications and variations will be evident to those skilled in the art, that fall within the scope of the following claims: 
     
       1. Method of measuring a curvature of a surface, comprising:
 illuminating the surface with electromagnetic radiation; 
 reflecting the electromagnetic radiation from the surface; 
 forming on a detector a defocused image of the surface, wherein the defocused image comprises an intensity distribution defined by Fresnel diffraction, wherein said intensity distribution is formed by the reflected electromagnetic radiation having been at least one of refracted by a lens or reflected off of a curved mirror positioned in the path of the reflected electromagnetic radiation at a distance from the detector sufficient to form the defocused image; 
 obtaining data for the intensity distribution; and 
 determining information relating to the curvature of the surface using the obtained data; wherein determining information relating to the curvature of the surface comprises:
 processing the obtained data to calculate a figure of merit indicative of the size of the intensity distribution in at least one dimension; and 
 determining information relating to the curvature of the surface using the calculated figure of merit. 
 
 
     
     
       2. Method as claimed in  claim 1 , wherein determining information relating to the curvature of the surface further comprises determining an absolute value of a curvature parameter. 
     
     
       3. Method as claimed in  claim 1 , wherein determining information relating to the curvature of the surface further comprises:
 determining a scaling factor for the intensity distribution, and measuring the curvature of the surface by comparing the scaling factor with a predetermined formula. 
 
     
     
       4. Method as claimed in  claim 1 , wherein said surface is a surface of a cantilever. 
     
     
       5. Method as claimed in  claim 4 , wherein the cantilever has a length of 500 micron or less. 
     
     
       6. Method as claimed in  claim 4 , wherein said cantilever is one of a plurality of cantilevers, wherein the method comprises illuminating said plurality of cantilevers. 
     
     
       7. Method as claimed in  claim 6 , wherein the method comprises forming images for each cantilever, wherein there is no substantial overlap between images for each cantilever. 
     
     
       8. Method as claimed in  claim 6 , wherein the method comprises illuminating at least a part of an array of cantilevers comprising said plurality of cantilevers. 
     
     
       9. Method as claimed in  claim 1 , wherein the intensity distribution is a mapping of an intensity distribution formed at a distance z from the surface, wherein z is less than 100 mm. 
     
     
       10. Method as claimed in  claim 1 , further comprising determining information relating to the tilt of the surface using the obtained data. 
     
     
       11. Method as claimed in  claim 1 , further comprising:
 reflecting electromagnetic radiation from a second surface to form a second intensity distribution defined by Fresnel diffraction, 
 wherein the formed defocused image further comprises said second intensity distribution; 
 obtaining data for the second intensity distribution; 
 determining information relating to the curvature of the second surface using the obtained data, 
 wherein said intensity distribution and said second intensity distribution are formed concurrently and do not substantially overlap with one another. 
 
     
     
       12. Method as claimed in  claim 11 , comprising:
 forming a first diffraction image, wherein said first diffraction image is formed by the electromagnetic radiation which has been reflected from the first surface; 
 forming a second diffraction image, wherein said second diffraction image is formed by the electromagnetic radiation which has been reflected from the second surface, wherein the first and second diffraction images are formed concurrently; 
 obtaining data for the first and second diffraction images; 
 determining information relating to the curvature of the first and second surfaces using the obtained data, 
 wherein the first and second diffraction images do not substantially overlap with one another. 
 
     
     
       13. A method according to  claim 12 , wherein the first surface is a surface of a first cantilever, and the second surface is a surface of second cantilever. 
     
     
       14. A method as claimed in  claim 13 , wherein the first and second cantilevers are individual members of a cantilever array. 
     
     
       15. A method as claimed in  claim 14 , comprising forming a defocused focus image of the array, wherein the defocused image of the array includes the first diffraction image and the second diffraction image. 
     
     
       16. Method according to  claim 11 , wherein obtaining data for the first and second intensity distributions comprises:
 identifying a plurality of regions in the defocused image, each region comprising a sub-image corresponding to a single one of said surfaces; 
 calculating a figure of merit indicative of the size of each sub-image in at least one dimension; and wherein the method further comprises: 
 determining information relating to the curvature of at least one surface using the figure of merit. 
 
     
     
       17. Method as claimed in  claim 16 , wherein identifying a plurality of regions in the image comprises:
 processing the image data to align sub-images for each surface; 
 obtaining a histogram of intensity per pixel column; and 
 identifying said plurality of regions using the histogram. 
 
     
     
       18. Apparatus for measuring the curvature of a non-planar surface, comprising:
 an electromagnetic radiation source configured to reflect electromagnetic radiation off of the non-planar surface; 
 one or more lenses or curved mirrors positioned in the path of the reflected electromagnetic radiation and at a distance from the detector sufficient to form the defocused image to produce a defocused image of the non-planar surface; 
 a detector positioned to receive and obtain data regarding the defocused image, wherein the defocused image comprises an intensity distribution defined by Fresnel diffraction, and wherein the one or more lenses or curved mirrors are positioned in the path of the reflected electromagnetic radiation at a distance from the detector sufficient to form the defocused image of the non-planar surface; 
 and 
 a processor to determine information relating to the curvature of the surface using the obtained data. 
 
     
     
       19. Apparatus as claimed in  claim 18 , wherein the sample comprises:
 a cantilever 
 of an atomic force microscope. 
 
     
     
       20. The apparatus of  claim 18 ,
 further configured to form, concurrently with the first intensity distribution, a second intensity distribution defined by Fresnel diffraction, wherein said second intensity distribution is formed by electromagnetic radiation reflected from a second surface; 
 wherein the formed defocused image further comprises said second intensity distribution; 
 wherein the detector is further configured to obtain image data for the second intensity distribution; 
 wherein the processor is further configured to determine information relating to the curvature of the first and second surfaces using the image data; and 
 wherein the detector and the one or more lenses or curved mirrors are configured so that the first and second intensity distributions do not substantially overlap with one another. 
 
     
     
       21. The apparatus of  claim 20 , further comprising:
 a sample comprising one or more target substances and a cantilever array having a plurality of cantilevers, each of said plurality of cantilevers being configured to change in curvature as a function of the concentration of one or more bio-chemical substances. 
 
     
     
       22. A system for detecting the presence of absence of a target substance in a fluid, comprising:
 a sample comprising a surface in contact with the fluid and configured to change in curvature as a function of the presence or absence of said target substance; 
 an apparatus for measuring the curvature of the surface comprising:
 an electromagnetic radiation source configured to reflect electromagnetic radiation off of the non-planar surface; 
 one or more lenses or curved mirrors positioned in the path of the reflected electromagnetic radiation and at a distance from the detector sufficient to form the defocused image to produce a defocused image of the non-planar surface; 
 a detector positioned to receive and obtain data regarding the defocused image, wherein the defocused image comprises an intensity distribution defined by Fresnel diffraction, and wherein the one or more lenses or curved mirrors are positioned in the path of the reflected electromagnetic radiation at a distance from the detector sufficient to form the defocused image of the non-planar surface; and 
 a processor to determine information relating to the curvature of the surface using the obtained data. 
 
 
     
     
       23. A system comprising:
 a surface configured to change in curvature as a function of at least one of force, temperature, strain, surface stress, or as a function of the presence of absence of a target substance or the concentration of one or more substances; 
 an apparatus for measuring the curvature of the surface comprising:
 an electromagnetic radiation source configured to reflect electromagnetic radiation off of the non-planar surface; 
 one or more lenses or curved mirrors positioned in the path of the reflected electromagnetic radiation and at a distance from the detector sufficient to form the defocused image to produce a defocused image of the non-planar surface; 
 a detector positioned to receive and obtain data regarding the defocused image, wherein the defocused image comprises an intensity distribution defined by Fresnel diffraction, and wherein the one or more lenses or curved mirrors are positioned in the path of the reflected electromagnetic radiation at a distance from the detector sufficient to form the defocused image of the non-planar surface; and 
 a processor to determine information relating to the curvature of the surface using the obtained data.